Simplify the following expression: $ t = \dfrac{-5p + 7}{-7p - 7} + \dfrac{-9}{4} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-5p + 7}{-7p - 7} \times \dfrac{4}{4} = \dfrac{-20p + 28}{-28p - 28} $ Multiply the second expression by $\dfrac{-7p - 7}{-7p - 7}$ $ \dfrac{-9}{4} \times \dfrac{-7p - 7}{-7p - 7} = \dfrac{63p + 63}{-28p - 28} $ Therefore $ t = \dfrac{-20p + 28}{-28p - 28} + \dfrac{63p + 63}{-28p - 28} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-20p + 28 + 63p + 63}{-28p - 28} $ $t = \dfrac{43p + 91}{-28p - 28}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-43p - 91}{28p + 28}$